Advances in Mathematical Fluid Mechanics

Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

Authors: Bellout, Hamid, Bloom, Frederick

  • Exceptionally well-written and strong presentation of the case for bipolar fluids
  • Provides a comprehensive and consolidated reference for the multipolar fluid model
  • Presents applications of the model to standard as well as non-standard problems​
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About this book

The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids  is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model.
 
A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory.
 
This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.

Reviews

From the book reviews:

“The authors present some results obtained on incompressible nonlinear bipolar fluid flows. The book contains six chapters and three appendices. … This book will be a valuable resource for applied mathematicians, fluid dynamicists and engineers with an interest in non-Newtonian fluid mechanics.” (Valeriu Al. Sava, zbMATH, Vol. 1291, 2014)

Table of contents (6 chapters)

  • Incompressible Multipolar Fluid Dynamics

    Bellout, Hamid (et al.)

    Pages 1-77

  • Plane Poiseuille Flow of Incompressible Bipolar Viscous Fluids

    Bellout, Hamid (et al.)

    Pages 79-136

  • Incompressible Bipolar Fluid Dynamics: Examples of Other Flows and Geometries

    Bellout, Hamid (et al.)

    Pages 137-237

  • General Existence and Uniqueness Theorems for Incompressible Bipolar and Non-Newtonian Fluid Flow

    Bellout, Hamid (et al.)

    Pages 239-345

  • Attractors for Incompressible Bipolar and Non-Newtonian Flows: Bounded Domains and Space Periodic Problems

    Bellout, Hamid (et al.)

    Pages 347-433

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-00891-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-319-00890-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-319-34553-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow
Authors
Series Title
Advances in Mathematical Fluid Mechanics
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
Distribution Rights
Distribution rights for India: Delhi Book Store, New Delhi, India
eBook ISBN
978-3-319-00891-2
DOI
10.1007/978-3-319-00891-2
Hardcover ISBN
978-3-319-00890-5
Softcover ISBN
978-3-319-34553-6
Series ISSN
2297-0320
Edition Number
1
Number of Pages
XX, 569
Number of Illustrations and Tables
16 b/w illustrations
Topics